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Fermilab FERMILAB-THESIS-1999-41 CP Asymmetry in the Decay K L π + π - e + e - DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL OF OSAKA UNIVERSITY IN CANDIDACY FOR THE DEGREE OF DOCTOR OF SCIENCE By Katsumi Senyo 1999

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  • Fermilab FERMILAB-THESIS-1999-41

    CP Asymmetry in the Decay KL +e+e

    DISSERTATION SUBMITTED TO

    THE GRADUATE SCHOOL OF OSAKA UNIVERSITY

    IN CANDIDACY FOR THE DEGREE OF

    DOCTOR OF SCIENCE

    By

    Katsumi Senyo

    1999

  • 1

  • Acknowledgments

    I first appreciate Prof. Yorikiyo Nagashima, for all research opportunity in HEP field. I was really

    enlightened by his expertise. T. Yamanaka gave me a chance to work on indirect CP violation in

    a rare K decay experiment, instead of a B physics experiment. I thank him for his supervision

    of my study, and really enjoy a chat with him about experimental and theoretical science. Also,

    I remember the trans-pacific midnight proofreading of the thesis, especially in the last one week

    before the defense.

    Other stuffs in Osaka University, J. Haba, M. Takita, M. Hazumi and I. Suzuki gave me very

    useful advises and suggestions, in and out of physics. Their humor and wit always relaxed me.

    Thankfully, S. Tsuzuki supported my study from Osaka.

    My works done at Fermilab, especially the physics analysis, were mostly supported by V. ODell.

    The discussion with her was really fun. I enjoyed the life on the crossover with L. Bellantoni, P.

    Shanahan, M. Pang, and R. Ben-David. I thank their kindness. I also appreciate KTeV people

    on the thirteen floor and new muon lab. Of course, I thank all of people working at the KTeV

    experiment. Without their efforts, I could not successfully finish my thesis like this.

    I feel relaxed with T. Nakaya and K. Hanagaki, and previous generation of graduate students

    in Osaka University. Their friendship and useful suggestion encouraged me in any phases of my

    analysis. I studied much from them. I thank graduate students in Osaka University for their

    cooperation for years.

    My parents, Sakae and Kotaro Senyo, patiently waited for my graduation. Their supports

    greatly heartened me. I hope they proud of me.

    Finally, I thank my wife, Sachiko, and her tenderness. Actually, I enjoyed the life with her in

    Chicago. It was very tough time in my life, but we will long for our precious time and good friends

    in Fermilab.

    2

  • Contents

    1 Introduction 1

    1.1 C, P, and CP Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.2 CP violation in Neutral Kaon System . . . . . . . . . . . . . . . . . . . . . . . . . 2

    1.2.1 Indirect CP Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    1.2.2 Direct CP Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    1.2.3 Experimental Results of Indirect CP Violation . . . . . . . . . . . . . . . . 5

    1.3 KL +e+e Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.3.1 Decay Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    1.3.2 Indirect CP violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    1.3.3 Direct CP violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    1.3.4 gM1 Form Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

    1.3.5 Experimental Status of KL +e+e . . . . . . . . . . . . . . . . . . . 121.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

    1.4.1 Purpose of This Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

    1.4.2 Overview of This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

    2 Experiment 14

    2.1 KL Beam Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    2.1.1 Beam Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    2.1.2 Sweeper and Collimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    2.1.3 Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.2 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.2.1 Charged Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

    2.2.2 Trigger hodoscopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    2.2.3 Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . 22

    2.2.4 Photon Vetoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

    2.2.5 Hadron/Muon vetoes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    2.3 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    2.3.1 Level 1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

    2.3.2 Level 2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    i

  • 2.3.3 Trigger Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    2.3.4 Calibration Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    2.4 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

    2.4.1 Frontend and DAQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

    2.4.2 Level 3 filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

    2.5 Physics Run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

    3 Monte Carlo Simulation 35

    3.1 Kaon production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

    3.2 The Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

    3.2.1 KL +e+e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2.2 KL +0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2.3 Particle Tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    3.3 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    3.3.1 Photon Veto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    3.3.2 Drift Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    3.3.3 CsI calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

    3.4 Accidentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

    3.4.1 Accidental Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

    3.4.2 Accidental Overlay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

    4 Event Reconstruction 43

    4.1 Track Candidate Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    4.1.1 Hit Pairing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

    4.1.2 Finding Y track candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    4.1.3 Finding X track candidates . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

    4.2 Cluster Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    4.3 Track-Cluster Matching and Vertex Finding . . . . . . . . . . . . . . . . . . . . . . 45

    4.4 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    5 Event Selection 48

    5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

    5.2 Basic Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

    5.2.1 Fiducial Volume Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

    5.2.2 Trigger Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

    5.2.3 Consistency Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

    5.3 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

    5.3.1 MK Invariant Mass Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    5.3.2 Total Momentum Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    5.3.3 Vertex 2 Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    ii

  • 5.3.4 Mee Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

    5.3.5 p2t Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

    5.3.6 Pp0kine Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

    5.3.7 Optimization of p2t and Pp0kine Cuts . . . . . . . . . . . . . . . . . . . . . 58

    5.4 Acceptance and Data After Final Cuts . . . . . . . . . . . . . . . . . . . . . . . . . 60

    5.5 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

    5.5.1 Background Level from Each Source . . . . . . . . . . . . . . . . . . . . . . 62

    5.5.2 Background estimation with sideband fit . . . . . . . . . . . . . . . . . . . . 63

    5.5.3 Summary of Background Level . . . . . . . . . . . . . . . . . . . . . . . . . 63

    5.6 KL Flux Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

    5.6.1 Acceptance and Flux Calculation . . . . . . . . . . . . . . . . . . . . . . . . 64

    5.6.2 Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

    5.6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

    6 Form Factor Measurement 70

    6.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

    6.2 Maximum Likelihood Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

    6.3 Data and Monte Carlo Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    6.4 Error on the Form Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

    6.4.1 Fitting Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

    6.4.2 Smearing by Detector Resolution . . . . . . . . . . . . . . . . . . . . . . . . 79

    6.4.3 Vertexing Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

    6.4.4 Drift Chamber Inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

    6.4.5 Momentum Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

    6.4.6 Physics Input Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

    6.4.7 Background Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

    6.4.8 Analysis Dependencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

    6.4.9 Systematic Uncertainty: Summary . . . . . . . . . . . . . . . . . . . . . . . 86

    6.5 Form Factor Measurement: Summary . . . . . . . . . . . . . . . . . . . . . . . . . 86

    7 Asymmetry Measurement 88

    7.1 Raw Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

    7.1.1 Raw Asymmetry Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 89

    7.1.2 Bias from Detector and Event Selection . . . . . . . . . . . . . . . . . . . . 89

    7.1.3 Origin of Raw Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

    7.2 Acceptance Corrected Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

    7.3 Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

    7.3.1 Smearing by Detector Resolution . . . . . . . . . . . . . . . . . . . . . . . . 98

    7.3.2 gM1 Form Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

    7.3.3 Vertexing Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

    iii

  • 7.3.4 Drift Chamber Inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

    7.3.5 Other Physics Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

    7.3.6 Background Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

    7.3.7 Analysis Dependency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

    7.3.8 Systematic Uncertainty: Summary . . . . . . . . . . . . . . . . . . . . . . . 104

    7.4 Asymmetry Measurement: Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 104

    8 Branching Ratio Measurement 105

    8.1 Event Selection and Background Estimation . . . . . . . . . . . . . . . . . . . . . . 105

    8.2 Systematic Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

    8.2.1 Drift Chamber Inefficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

    8.2.2 Vertexing Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

    8.2.3 Normalization Ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

    8.2.4 KL +e+e Monte Carlo Generation . . . . . . . . . . . . . . . . . . 1108.2.5 Background Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

    8.2.6 Analysis Dependency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

    8.2.7 External Systematic Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 113

    8.2.8 Systematic Uncertainty: Summary . . . . . . . . . . . . . . . . . . . . . . . 113

    8.3 Branching Ratio Measurement: Summary . . . . . . . . . . . . . . . . . . . . . . . 113

    9 Discussion 115

    9.1 Form Factor Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

    9.2 Asymmetry Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

    9.3 Branching Ratio Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

    9.4 Remarks and Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

    10 Conclusion 119

    A Maximum Likelihood Method 121

    A.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

    A.2 Use of Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

    A.3 Reduction of Monte Carlo Generation . . . . . . . . . . . . . . . . . . . . . . . . . 123

    A.4 Fit Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

    B Pp0kine: Kinematics with

    a Missing Particle 125

    iv

  • List of Figures

    1.1 KL + decay process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 The photon spectrum in KL +. . . . . . . . . . . . . . . . . . . . . . . . . 71.3 KL +e+e decay process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.4 Critical angles in KL +e+e. . . . . . . . . . . . . . . . . . . . . . . . . . . 101.5 E distribution of KL + in the kaon center-of-mass frame. . . . . . . . . . 12

    2.1 KTeV beamline and detector layout. . . . . . . . . . . . . . . . . . . . . . . . . . . 16

    2.2 KTeV E799-II Detector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

    2.3 A cross section of the drift chamber. . . . . . . . . . . . . . . . . . . . . . . . . . . 19

    2.4 TDC time distribution of drift chamber. . . . . . . . . . . . . . . . . . . . . . . . 20

    2.5 SOD distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    2.6 The V and V trigger hodoscope planes. . . . . . . . . . . . . . . . . . . . . . . . . 22

    2.7 The KTeV electromagnetic Calorimeter. . . . . . . . . . . . . . . . . . . . . . . . 23

    2.8 E/p for electrons in Ke3 decays, where E means an energy deposit in the calorimeter,

    and p denotes a momentum measured by the spectrometer. . . . . . . . . . . . . . 25

    2.9 The calorimeter intrinsic energy resolution measured in Ke3 events as a function of

    electron momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

    2.10 The schematic view of RC6, facing downstream. The beam passed through the inner

    aperture. The perimeter of outer circle fit right with the vacuum pipe. The other

    RCs were basically similar in a form but the dimensions seen in Table 2.2. . . . . . 27

    2.11 SA4 from upstream. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

    2.12 The Collar Anti just in front of the calorimeter. . . . . . . . . . . . . . . . . . . . . 27

    2.13 The HA hodoscope. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    2.14 The Mu2 counter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    2.15 Data acquisition system. Three planes were used for Level 3 trigger and the other

    was for online monitoring of the detector performance and online calibration. . . . 33

    3.1 Momentum distribution of the generated kaons. . . . . . . . . . . . . . . . . . . . . 37

    3.2 KL decay Z-distribution of Monte Carlo generated kaons. . . . . . . . . . . . . . . 37

    3.3 E/p distribution of hadronic shower samples . . . . . . . . . . . . . . . . . . . . . . 40

    3.4 Electromagnetic and hadronic shower comparison. . . . . . . . . . . . . . . . . . . 41

    v

  • 4.1 Schematic view of the classification of hit pairs. . . . . . . . . . . . . . . . . . . . . 44

    4.2 E/p comparison. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

    5.1 Mass distribution after basic cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

    5.2 Total momentum distribution of four charged tracks. . . . . . . . . . . . . . . . . . 54

    5.3 Total momentum from each background source. . . . . . . . . . . . . . . . . . . . . 54

    5.4 Vertex 2 distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

    5.5 Mee distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

    5.6 Mee distribution from each background source. . . . . . . . . . . . . . . . . . . . . 56

    5.7 p2t distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

    5.8 pt2 distribution from each background source. . . . . . . . . . . . . . . . . . . . . . 57

    5.9 Schematic view of Pp0kine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

    5.10 Pp0kine distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

    5.11 Pp0kine distribution from each background source. . . . . . . . . . . . . . . . . . . 59

    5.12 Invariant mass distribution after final cuts. . . . . . . . . . . . . . . . . . . . . . . 61

    5.13 Distribution of mass of +e+e. . . . . . . . . . . . . . . . . . . . . . . . . . . 65

    5.14 HCC threshold distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

    6.1 M distribution between data and Monte Carlo with a constant gM1 in the decay

    KL +e+e. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.2 The diagrams for the vector meson intermediate model. . . . . . . . . . . . . . . . 72

    6.3 The gM1 form factor effect in the decay KL +. . . . . . . . . . . . . . . . 736.4 Fit result of a1/a2 and a1 from two dimensional maximum likelihood method. . . . 75

    6.5 Comparison of various distributions between data and Monte Carlo. . . . . . . . . 76

    6.6 The comparisons of M distribution between data and Monte Carlo with and with-

    out the form factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

    6.7 Fit results of a1/a2 and a1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

    6.8 Fit results of a1/a2 and a1 for the ten pseudo data samples. . . . . . . . . . . . . . 80

    6.9 Data and Monte Carlo comparison in vertex 2 for KL +e+e. . . . . . . . 816.10 Data and modified Monte Carlo comparison in vertex 2 for KL +e+e. . . 816.11 Data and Monte Carlo comparison for Mee distribution in the decay KL +0D. 836.12 Data and Monte Carlo comparison of track illumination at DC1 in Y view. . . . . 84

    6.13 Distributions of Mee from KL +0D of data and Monte Carlo. . . . . . . . 856.14 Averaged M as a function of (E1 + E2) for KL +0D data and Monte

    Carlo simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

    7.1 distribution of data overlaid with the Monte Carlo. . . . . . . . . . . . . . . . . . 90

    7.2 Distribution of (2 cos sin ) from data, overlaid with the Monte Carlo. . . . . . . 90

    7.3 distribution of identified KL +0D. . . . . . . . . . . . . . . . . . . . . . . 927.4 Raw asymmetries at different mass regions. . . . . . . . . . . . . . . . . . . . . . . 92

    vi

  • 7.5 Relation between the input and raw asymmetry. . . . . . . . . . . . . . . . . . . . . 94

    7.6 Distributions of KL +e+e with respect to . . . . . . . . . . . . . . . . . . 967.7 Signal acceptance as a function of . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

    7.8 The distribution of acceptance corrected data. . . . . . . . . . . . . . . . . . . . 97

    7.9 The resolution effect causing wrong sign events. . . . . . . . . . . . . . . . . . . . . 100

    7.10 The difference between real and reconstructed . . . . . . . . . . . . . . . . . . . 100

    7.11 X track swapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

    7.12 The resolution effect causing wrong sign events with Mee < 2MeV/c2. . . . . . . . 102

    7.13 The difference between real and reconstructed for events with Mee < 2MeV/c2. 102

    8.1 Invariant mass distribution after final cuts. . . . . . . . . . . . . . . . . . . . . . . 106

    8.2 Invariant mass distribution with 0.0001 < pt < 0.0002GeV2/c2. . . . . . . . . . . . 107

    8.3 Data and the Monte Carlo comparison after background subtraction. . . . . . . . . 108

    8.4 Comparison between data and Monte Carlo estimation in the sideband. . . . . . . 112

    9.1 Results on the DE form factor, a1/a2. . . . . . . . . . . . . . . . . . . . . . . . . . 116

    9.2 and DE branching ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

    vii

  • List of Tables

    2.1 Positions and dimensions of the spectrometer elements. . . . . . . . . . . . . . . . 18

    2.2 Positions and dimensions of the photon vetoes. . . . . . . . . . . . . . . . . . . . . 26

    2.3 Positions and dimensions of the detectors(downstream of the calorimeter). . . . . . 28

    2.4 The E799 four track trigger elements. . . . . . . . . . . . . . . . . . . . . . . . . . 30

    2.5 The KTeV-E799II run conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

    3.1 The parameters referred from Malensek [7] . . . . . . . . . . . . . . . . . . . . . . . 36

    5.1 Signal to background ratio matrix table. . . . . . . . . . . . . . . . . . . . . . . . . 60

    5.2 The signal acceptance at analysis each phase. . . . . . . . . . . . . . . . . . . . . . 62

    5.3 Backgrounds acceptance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

    5.4 Cuts for K0L +0D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.5 Summary of the background level at the flux measurement. . . . . . . . . . . . . . 66

    5.6 Summary of systematic uncertainty in the flux measurement. . . . . . . . . . . . . 68

    5.7 Summary of the flux calculation with K0L +0D. Expected background wasalready subtracted. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

    6.1 Fixed physics parameters in the maximum likelihood fit. Values are reported by the

    Particle Data Group(PDG) [9] and the theoretical prediction [22]. . . . . . . . . . 74

    6.2 Acceptance calculation dependency of the sample size. . . . . . . . . . . . . . . . . 78

    6.3 Smearing effect by the detector resolution. . . . . . . . . . . . . . . . . . . . . . . . 79

    6.4 Stability to parameter fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

    6.5 Background uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

    6.6 Deviations of analysis cut dependencies. . . . . . . . . . . . . . . . . . . . . . . . . 87

    6.7 Systematic uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

    7.1 Raw asymmetries at different mass regions. . . . . . . . . . . . . . . . . . . . . . . 91

    7.2 Comparison between the input and raw asymmetry. . . . . . . . . . . . . . . . . . . 93

    7.3 Asymmetries of various data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

    7.4 Experimental Input Parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

    7.5 Deviations of analysis cut dependencies in the acceptance corrected asymmetry. . . 103

    viii

  • 7.6 Summary of systematic uncertainties. . . . . . . . . . . . . . . . . . . . . . . . . . 104

    8.1 Background acceptance after final cut. . . . . . . . . . . . . . . . . . . . . . . . . . 107

    8.2 The signal acceptance at each analysis phase. . . . . . . . . . . . . . . . . . . . . . 108

    8.3 Stability to parameter fluctuations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

    8.4 Summary of analysis dependency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

    8.5 Summary of uncertainty in branching ratio measurement. . . . . . . . . . . . . . . 114

    ix

  • Abstract

    CP violation in an angluar asymmetry has been established in the decay KL +e+e based on1162 events. Measured CP asymmetry, which appeared in the angular distribution between normals

    to + and e+e planes, is 0.127 0.029(stat.) 0.016(syst.). The form factor of M1 directemission appeared in KL +( e+e) is determined as a1/a2 = 0.684+0.0310.043(stat.) 0.053(syst.) and a1 = 1.050.14(stat.)0.18(syst.). The branching ratio has also been determinedas Br(KL +e+e) = (3.55 0.11(stat.) 0.08(syst.internal) 0.14(syst.external)) 107.

  • Chapter 1

    Introduction

    The CP violation is a small effect, yet it has been one of the greatest discoveries in particle physics.

    Since its discovery in 1964, people have been eager for elucidating its origin, process and effect.

    Recently, we are finally recognizing its phenomenology in the electroweak physics. This thesis

    intends to show a part of such challenging efforts by exploring the decay KL +e+e.In this introduction, we cover theoretical backgrounds of KL +e+e decay process. It

    starts with a historical overview on C, P and CP violations. Next, we describe phenomenology of

    the neutral kaon system and CP violation. In addition, we briefly introduce recent experimental

    status of its direct and indirect CP violation effects. We then study the decay KL +e+eprocess and the technique to measure the CP violation effect in this decay mode. Finally, we glance

    the overview of this thesis.

    1.1 C, P, and CP Violation

    Most of the theories in particle physics declare the existence of some kinds of symmetries in the

    framework. However, observations of symmetry breakings in nature have been a guide to a new

    theory, which declares underlying symmetry in the more fundamental level.

    In particle physics, there are three interesting discrete symmetries; charge conjugation(C),

    parity, i.e., space inversion(P), and time reversal(T). These symmetry operations have eigenvalues

    of +1 and -1, called even and odd, respectively. Relativistic field theories require that the equations

    of motion must conserve its form under joint operations of C, P, and T. This is called a CPT

    theorem [1, 2]. The CPT theorem assures the equality of masses, lifetimes and magnitude of charges

    between particles and anti-particles. To date, no CPT violation has been observed experimentally.

    At the dawn of modern particle physics, any physical processes were simply believed to be

    invariant under each operation of C, P, and T. In the early 50s, strange particles were found.

    Among them were those named and . Although they had the same lifetime and mass, these

    two particles decayed into different parity states, actually two pions and three pions respectively,

    1

  • so that they were considered as different particles. In 1956, Lee and Yang insisted that no obvious

    evidence for the parity conservation had been found in the weak interaction [3]. They proposed

    experiments to test parity conservation in decays of a polarized nuclei and so on. An experiment

    to test the invariance was performed in 1957 by Wu et al.[4], using the Gamow-Teller transition in60Co polarized nuclei, and they discovered the parity violation in the decay. With further studies

    on the weak interaction, it was found that C and P symmetries were fully violated, but still CP

    was thought to be invariant at that time.

    In 1964, even CP symmetry was found to have a small but finite amount of violation in the

    long-lived neutral kaon system [5]. The long-lived kaon, KL, which had been believed to be a pure

    CP odd state, was found to decay into CP even two pion state. Up to date, C, P and CP violations

    are known in the weak interaction only, and especially, CP violation has been observed only in the

    neutral kaon system.

    Since the discovery of the CP violation, people have been exploring its mechanism and origin,

    and recently with sophisticated detectors and techniques, we have accumulated enough knowledge

    to almost clarify the nature of CP violation in the electroweak interaction.

    1.2 CP violation in Neutral Kaon System

    In this section, we explain phenomenological description of CP violation in the neutral kaon system

    and recent experimental status of them. First, we start with the phenomenology.

    There are two kinds of neutral kaons in different eigenstates which are distinguished with

    strangeness of +1 and -1:

    |K0 >= |(d, s) >, |K0 >= |(d, s) > . (1.1)

    They are easily produced through the strong interaction, where the strangeness is conserved.

    K0 and K0 are defined as CP conjugate to each other:

    CP |K0 > = |K0 >, (1.2-a)CP |K0 > = |K0 >, (1.2-b)

    with phase ambiguity, where CP means the CP transforming operation. Here we can choose the

    phase as above since the phase is not observable. If we define K1 and K2 as

    |K1 > = 12(|K0 > +|K0 >), (1.3-a)

    |K2 > = 12(|K0 > |K0 >), (1.3-b)

    these are CP eigenstates like

    CP |K1 > = |K1 > (CP even), (1.4-a)CP |K2 > = |K2 > (CP odd). (1.4-b)

    2

  • K0 and K0 can transit to each other through K0 (2, 3 etc.) K0, implying < K0|H |K0 >6=0, where H includes the strong interaction HS , and the weak interaction HW causing decays. This

    phenomenon is called mixing. Naturally, the mixing includes S = 2 transition.

    To understand the mixing in the neutral kaon system in the rest frame, let us start from a

    time-dependent Schrodinger equation with two quantum states including the mixing like [6];

    (t) = (t)|K0 > +(t)|K0 >,

    id

    dt

    (

    )=

    (< K0|H |K0 > < K0|H |K0 >< K0|H |K0 > < K0|H |K0 >

    )(

    )

    =

    (M11 M12

    M21 M22

    )(

    ). (1.5)

    Taking the second order of the weak interaction, we can rewrite Mij as a combination of two

    Hermitian matrices, Mij and ij ;

    Mij = Mij iij/2 (1.6-a)Mij = Miij+ < i|HW |j > +

    n 6=K0,K0

    P< i|HW |n >< n|HW |j >

    Mi En (1.6-b)

    ij = 2

    n 6=K0,K0(Mi En) < i|HW |n >< n|HW |j >, (1.6-c)

    where P means a principal value. The M is called mass matrix and is called decay matrix, and

    its off-diagonal elements give the mixing between K0 and K0 states.

    We now consider the eigenvalue of this equation. We can rewrite

    (t) = (t)|K1 > +(t)|K2 >= (t)|K0 > +(t)|K0 > (1.7-a)

    id

    dt

    (

    )=

    (S 0

    0 L

    )(

    )(1.7-b)

    S = mS iS/2, L = mL iL/2, (1.7-c)

    where the eigenvalues are, in general, complex and mL,S , L,S are real.

    Since only K1 can decay into *1, the Q value of K1 is larger than that of K2. Therefore, K2lives longer than K1(1 2). Until CP violation was observed in 1964, it was believed that thelong lived kaon could have decayed only into odd CP state.

    *1Here is an explanation of CP state in 2 and 3 system:

    1) 2: P = and C0 = 0, and C = . Because of Bose statistics, C is equivalent to P in + system.So CP (+) = (1)2` = +1, where ` is an orbit angular momentum. For 20, an orbit angular momentum mustbe an even number from the Bose symmetry, thus CP00 = +1.

    2) 3: For +0, assuming the angular momentum of + is ` and a relative angular momentum between a0 and + system is L, it gives CP (+0) = (1)2`+L+1. Since the angular momentum barrier forces to beL = 0 and ` = 0, CP becomes negative. For 30, like 1), ` becomes zero. So L = 0 since the total momentum must

    be zero. Thus, CP (000) must be negative.

    3

  • 1.2.1 Indirect CP Violation

    CP violation was first observed as a signature of long lived kaons decaying into CP even two pion

    final states. This phenomenon is explained if the long lived kaon, KL, is almost K2, but has an

    admixture of CP even K1 state.

    |KL >= 11 + ||2 (|K2 > +|K1 >) =

    12(1 + ||2) ((1 + )|K

    0 > (1 )|K0 >), (1.8-a)

    |KS >= 11 + ||2 (|K1 > +|K2 >) =

    12(1 + ||2) ((1 + )|K

    0 > +(1 )|K0 >), (1.8-b)

    where we assume CPT invariance. The contamination of K1 in the KL causes the decay into CP

    even final state, such as two pions, and amount of CP asymmetry is determined by . The CP

    violation from the mixing asymmetry is called indirect CP violation.

    1.2.2 Direct CP Violation

    The CP violation can be observed in a decay process also. This is called direct CP violation. If

    we define decay amplitudes to a CP eigenstate fCP like

    afCP = < fCP |Heff |K0 >afCP = < fCP |Heff |K0 >, (1.9)

    direct CP violation means afCP 6= afCP . Let us choose CP even final state, fCP , and define a CPviolating parameter:

    rfCP =< fCP |Heff |KL >< fCP |Heff |KS >. (1.10)

    Substituting Equation 1.9 into Equation 1.10, we obtain

    rfCP =(afCP afCP ) + (afCP + afCP )(afCP + afCP ) + (afCP afCP )

    . (1.11)

    If afCP 6= afCP , not only term(i.e., indirect CP violation) but also the difference between afCPand afCP contribute to the CP violation. Defining the decay asymmetry as

    fCP =afCP afCPafCP + afCP

    , (1.12)

    we can rewrite Equation 1.10 as

    rfCP = + fCP1 + fCP

    + fCP (1.13)

    where we used an empirical fact that is very small, 103. Equation 1.13 shows CP violationcan be separated into two effects.

    The direct CP violation was predicted by many people. Among them, Kobayashi and Maskawa

    showed that CP violation results by extending the quark mixing from four quarks to six quarks [33],

    4

  • which is now a part of the Standard Model. Since then, many searches have been performed, and

    finally, a finite direct CP violation has been reported by NA31 and KTeV collaborations in the

    neutral kaon system [34, 35].

    1.2.3 Experimental Results of Indirect CP Violation

    We briefly introduce experimental results in the field of indirect CP violation. We here show

    results from KL , a semi-leptonic K decay, and a radiative K decay, KL +. Thedecay KL + is strongly related to the decay KL +e+e, which is the topic of thisthesis.

    Indirect CP violation in KL

    CP violation was first observed in KL + by V.L.Fitch, J.W.Cronin et al. in 1964[5]. Thiswas a direct observation of indirect CP violation with CP even final state, +. This implies

    that KL includes the CP even small component of K1 which decays into + final state.

    Now the branching ratio is known to be [9]

    BR(KL +) = (2.067 0.035) 103. (1.14)

    CP violation was also observed in a final state, KL 00,

    BR(KL 00) = (9.36 0.20) 104. (1.15)

    The related useful CP violation parameters are also provided from the decay amplitudes:

    + Amp(KL +)

    Amp(KS +) = |+| exp(i+),

    00 Amp(KL 00)

    Amp(KS 00) = |00| exp(i00).

    Recent results of these parameters are [9]

    |+| = (2.285 0.019) 103, + = 43.5 0.6,|00| = (2.275 0.019) 103, 00 = 43.4 1.0.

    Experimentally, a simultaneous collection of KL +, 00 and KS +, 00 decaysgives more precise measurements of the ratio, |00/+|, and the phase difference, 00 + [9]:

    | 00+

    | = 0.9956 0.0023, = 0.1 0.8.

    5

  • Indirect CP violation in KL `

    Another place to observe the CP violating effect is the charge asymmetry in kaon semileptonic

    decay, KL `. The charge asymmetry is defined as

    (KL `+`) (KL +``)

    (KL `+`) + (KL +``) . (1.16)

    These decay amplitudes indicate |K0 > and |K0 > composition of the KL, since an `+ can comeonly from a K0 decay, while ` can come only from K0 decay, as long as the S = Q rule

    holds. CPLEAR experiment at CERN reported that a deviation from S = Q rule in K decay is

    consistent with zero [10]. Therefore, the charge asymmetry is calculated from relative amplitudes

    of 1 + for K0 `+`, and 1 for K0 +`e:

    =|1 + |2 |1 |2|1 + |2 + |1 |2 2Re(). (1.17)

    Averaging the results from KL e(called Ke3), and KL (called K3),the experimental result was reported [9]:

    = (3.27 0.12) 103. (1.18)

    Using the phase of , this corresponds to || = (2.25 0.09) 103.These facts indicate that the same mixing mechanism is(at least) mostly responsible for CP

    violation effects in KL and the semileptonic decays.

    CP violation in KL +

    The decay process of KL + consists of (a) an inner bremsstrahlung(IB) component as-sociated with the CP violating decay, KL +, and (b) an M1 direct photon emission(DE)component of a CP conserving magnetic dipole moment [29](Figure 1.1)*2.

    The simultaneous existence of IB and DE amplitudes implies that the final state contains both

    CP = +1 and 1 states.The radiative photon spectrum from this decay mode becomes a superposition of these two

    amplitudes. The photon spectrum of KS,L + in the kaon center-of-mass system measuredby Fermilab E731 experiment is shown in Figure 1.2 [37]. The dotted line is obtained from the

    KS + photon spectrum, which is completely dominated by IB component. The datapoints indicate the E spectrum for the KL data. For the KL decay, there is an enhancement in

    the higher photon energy region over KS +. This is naturally understood to be the DEcomponent in the KL decay.

    Experimental results [36, 37, 38] on the branching ratio of KS + is(KS +, E > 20MeV)

    (KS +) = (7.10 0.16) 103(IB), (1.19)

    *2General formalism on radiative K decays is found in Ref. [20, 21]. In this thesis, in accordance with Ref. [29],

    we take the highest order of the magnetic dipole expansion, M1, which corresponds to a final state with a CP

    eigenstate, CP = (1)1 = 1. Note that the bremsstrahlung amplitude only includes CP even states.

    6

  • KL

    +

    a) Bremsstrahlung

    KL

    +

    b) M1 Direct Photon Emission

    Figure 1.1: Major KL + decay process. (a) an inner bremsstrahlung(IB) componentassociated with the CP violating decay, KL +, and (b) an M1 direct photon emission(DE)component of a CP conserving magnetic dipole moment.

    Figure 1.2: The photon spectrum in KL + [37]. The data points indicate the E spectrumfor the KL data. The dotted line is the same spectrum for the KS data, rescaled to the KL data.

    7

  • corresponding to the IB term. The QED prediction of this ratio is 7.01 103 [39], in goodagreement with the experimental result. The KL data was fitted with IB component from KSdata and a pure DE spectrum based on Ref. [29]:

    (KL +, E > 20MeV)(KL +) = (7.31 0.38) 10

    3(IB) (1.20-a)

    +(15.7 0.7) 103(DE) [37]. (1.20-b)

    This indicates the existence of two components in the KL decay.

    1.3 KL +e+e DecayThis section describes a theoretical and experimental interpretation for the decay KL +e+efrom an aspect of CP violation.

    In the previous section, we looked at theoretical and experimental results of KL +. Ifwe consider a virtual transition of the photon, e+e, another CP violating effect will appearin this decay. Here, we explain how CP violating effect arises in this decay.

    1.3.1 Decay Processes

    We start this section with a brief introduction to the theoretical overview of the physics process

    in KL +e+e. We first define decay amplitudes contributing to this decay. Similarlyto the decay KL +, the most dominant contribution is the M1 magnetic dipole directemission(DE) and the inner bremsstrahlung photon emission(IB).

    The dominant decay amplitude of

    KL(P) +(p+)(p)e+(k+)e(k) (1.21)

    has the form

    M(KL +e+e) = Mbr + Mmag, (1.22)

    where

    Mbr = e|fS|gBR[ p+p+ k

    pp k ]

    e

    k2(k)(k+), (1.23-a)

    Mmag = e|fS|gM1M4K

    kp+p

    e

    k2(k)(k+). (1.23-b)

    The terms Mbr and Mmag denote the bremsstrahlung and magnetic dipole, respectively. Thecoefficients appearing there are

    gBR = +ei0 ,

    gM1 = i(0.76)ei1 ,

    8

  • and |fS | is defined by

    (KS +) = |fs|2

    16mK[1 4m

    2

    m2K]. (1.25)

    The is defined as the ratio of amplitudes Amp(KL +)/Amp(KS +) as shownin Section 1.2.3, and 0(1) is a phase shift in the final-state interactions in the system with

    I = 0(1) wave state.

    KL

    +

    e+

    e-

    a) Bremsstrahlung

    KL

    +

    e+

    e-

    b) M1 Direct Photon Emission

    KL

    +

    e+

    e-

    c) E1 Direct Photon Emission

    KL

    +

    e+

    e-

    d) K0 Charge Radius

    KS

    KL

    +

    e+

    e-

    e) SD Direct CP Violation

    Figure 1.3: KL +e+e decay process. Besides major contributions of a) InnerBremsstrahlung and b) M1 direct emission, there are other small contributions.

    In addition, there are three small contributions; E1 electro dipole direct emission, charge radius

    and short distance direct CP violating amplitudes.

    By integrating over all parameters, the branching ratio is calculated as

    Br(KL +e+e) 3 107 [22, 23]. (1.26)

    1.3.2 Indirect CP violation

    Here we define critical parameters in KL +e+e. This decay kinematics is defined com-pletely with five kinematical parameters; invariant mass of +, invariant mass of e+e, an angle

    + between the directions of electrons and + in the pions center-of-mass frame, and an angle

    9

  • e+ between the directions of pions and e+ in the electrons center-of-mass frame. The angle ,

    which is of most interest in this thesis, is defined in terms of unit vectors constructed from the

    pion momenta p and lepton momenta k in the KL rest frame:

    n = (p+ p)/|p+ p|, n` = (k+ k)/|k+ k|,z = (p+ + p)/|p+ + p|,

    sin = n n` z, cos = n n`. (1.27)Thus, the angle is simply understood as an angle defined between normals to + and e+e

    decay planes in the KL rest frame. The schematic view of these angles is shown in Figure 1.4.

    +

    e-

    -

    e+

    KL

    KL

    +

    -

    e+ e-P

    +

    KL

    + -Pe+

    e+

    e-

    is an angle between the normals to the ee and planes in Kaon center of mass frame.

    + is an angle between a center of mass of two electrons and + in pions' center of mass frame.

    e+ is an angle between a center of mass of two pions and e+ in electrons' center of mass frame.

    Figure 1.4: Critical angles in KL +e+e.

    Integrating over all kinematic variables except for , and ignoring small contributions, the

    differential cross section in terms of these angles is written as follows;

    dd

    = 1 cos2 + 2 sin2 + 3 sin cos. (1.28)

    To identify the CP-violating terms in this expansion, we write the terms under the CP transfor-

    mation, p p, k k, which gives;cos + cos,sin sin. (1.29)

    10

  • Those constants were evaluated numerically in Ref. [23]. The 3 is the CP violating contribution,

    which is caused by the interference between IB and DE terms. In this sense, this is indirect CP

    violation. This contribution gives the angular asymmetry of

    Asym. =

    /20

    ddd

    /2

    ddd /2

    0ddd +

    /2

    ddd

    14% [22, 23], (1.30)

    where we folded the distribution within 2 < < 0 over 0 < < 2 for simplicity. This suggeststhat there is a large CP violating effect in this decay mode.

    1.3.3 Direct CP violation

    The angle is related to indirect CP violation, while + and e+ is expected to exhibit direct CP

    violation by interference between short-distance direct CP violating term and other contributions

    at very small level [23]. The theory suggests that the interference can be at most of order 106 as

    compared with the DE contribution. In addition, the direct CP violating effect does not contribute

    to the angular asymmetry of , shown in Equation 1.30. Therefore, the direct CP violating effect

    can be neglected in this study.

    1.3.4 gM1 Form Factor

    The theoretical calculations [22, 23] for the angular asymmetry and branching ratio of KL +e+e used a constant form factor gM1 for the M1 direct emission contribution, which was

    taken from the experimental result of KL + [22, 37]. However, an effect of vector mesonintermediate contribution was predicted [29] and observed [37] in the parent process, KL +.The form factor gM1 is modified as;

    gM1 gM1 FF = a1[(M2 M2K) + 2MKE ]1 + a2, (1.31)

    where M is the mass of vector meson, MK is the mass of kaon and E is the energy of the

    photon in the KL rest frame. Figure 1.5 shows distributions of E with vector meson intermediate

    contribution or a constant gM1 [37]. Clearly, inclusion of the vector meson effect in the form

    factor gives a better agreement.

    Besides KL +, the form factor gM1 can be independently measured with KL +e+e, in principle. The measurement should improve the estimate of the branching ratio

    and CP violating asymmetry of KL +e+e. From a point of view of our experiment, theuncertainty in gM1 gave an uncertainty in the branching ratio measurement up to 10%, while the

    expected statistical uncertainty would be 3%. The accuracy of the branching ratio measurement

    would be systematic dominant unless we improve the accuracy of gM1 form factor.

    11

  • Figure 1.5: E distribution of KL + in the kaon center-of-mass frame [37]. Dots are fromdata and dotted histograms are from Monte Carlo simulation. a)Monte Carlo with a form factor

    taking account of vector meson intermediate. b)Monte Carlo with a constant gM1.

    1.3.5 Experimental Status of KL +e+e

    The decay KL +e+e was first observed in 1998 by the KTeV collaboration with 46events [40] based on one day of data. The branching ratio was reported as:

    Br(KL +e+e) = (3.2 0.6(stat.) 0.4(syst.)) 107, (1.32)

    and this result agrees well with theoretical predictions, 3 107. However, statistics was notenough to evaluate the CP violating effect as well as the M1 direct emission form factor.

    1.4 Summary

    1.4.1 Purpose of This Study

    The decay KL +e+e is a fruitful field to explore CP violation in particle physics. Thismode is expected to show not only the fourth appearance of indirect CP violation, but also the

    significant CP violating effect.

    In addition, we can measure the form factor of M1 direct emission contribution in KL +e+e for the first time. This serves as a cross check of the form factor measured with

    KL +.

    12

  • Therefore, we will extract the following parameters of KL +e+e in this thesis:

    gM1 direct emission form factor.

    CP asymmetry in the angular distribution.

    Branching ratio.

    1.4.2 Overview of This Thesis

    We have discussed a theoretical aspect of KL +e+e, especially in CP violation and theform factor of M1 direct emission in this chapter. The rest of this thesis is devoted to describe

    new experimental results on KL +e+e in the KTeV experiment. In the following chapters,we start from explaining the detectors and run conditions. To understand detector response and

    acceptance, we utilized a Monte Carlo simulation, described in Chapter 3. Event reconstruction

    strategy and its scheme in the analysis are explained in Chapter 4. After that, we describe event

    selection to extract the signal.

    We proceed to physics analyses after the signal is obtained. First, we determine the form factor

    of M1 direct emission, and then feedback the measured parameters to the Monte Carlo simulation

    to improve its accuracy. Next, the angular asymmetry from the CP violating effect is evaluated

    and then, the branching ratio of this mode is determined. Finally, we summarize and discuss our

    results.

    13

  • Chapter 2

    Experiment

    This analysis on KL +e+e was performed as a part of a KL rare decay search programKTeVE799II in the Fermi National Accelerator Laboratory in 1997.

    This chapter describes the KTeV experiment and consists of three parts; short explanation of

    the data collecting strategy of KL +e+e, KLbeam and detector configuration, and datataking. We briefly mention the issues only related to the KL +e+e analysis. More detailedinformation about the KTeV experiment can be found in KTeV Technical Design Report [8] and

    KTeV internal documents.

    The final state of the decay KL +e+e consists of four charged tracks, +e+e. Thismeans if all four particles are identified and momenta are measured well, the whole kinematics and

    decay topology can be fully reconstructed.

    The decay KL +e+e was normalized by KL +0 with 0 Dalitz decay(denoting0D),

    0 e+e. In order to identify this decay, we should also detect a photon and measurethe photon energy and position. Since this decay has a final state of +e+e, this can be a

    significant background if one photon is missed. Therefore, photon vetoes were also required to veto

    events with escaping particles.

    From this regard, detector elements are required to have following functions:

    Momentum measurement of charged particles

    Identification of e, and .

    Photon energy and position measurement.

    Vetoes for the particles escaping from the detector.

    The KTeV detector was capable of satisfying these requirements. We here describe the KTeV

    detector system in this context.

    14

  • Before proceeding to the description of the experiment, the coordinate system of the KTeV

    experiment is defined here. A target is the origin of the coordinate, and downstream horizontal

    direction along beams is defined as the positive Z axis. The Y axis is defined as vertically pointing

    up. The three axes are defined with the right-handed coordinate system.

    2.1 KL Beam Production

    This section describes the neutral beam production.

    A 800 GeV primary proton beam was incident on a BeO target, to create various particles.

    Among them, neutral particles were selected by series of dipole magnets and collimators. The

    beam was then transported to the experimental hall.

    2.1.1 Beam Production

    Tevatron main ring in Fermilab provided 800GeV protons to KTeV. Protons were delivered over

    a 23 seconds spill in every 60 seconds. The intensity of the proton beam provided to KTeV

    was 2.5 1012 to 5.0 1012 protons per spill. Each spill has microstructure divided with 53 MHzTevatron radio frequency(RF), that is, a few nano second wide proton bunch delivered in every 19

    nsec.

    The primary proton beam was incident on the target with the vertical angle of 4.8 mrad in

    order to optimize both the higher neutral kaon flux and the better kaon to neutron flux ratio. The

    target was made of beryllium oxide(BeO) with the dimensions of 33 mm transverse to the protonbeam and 30 cm(0.9 interaction lengths) along the beam.

    2.1.2 Sweeper and Collimeter

    A sweeper magnet(NM2S1), which was located two meters downstream from the target, removed

    the remaining primary protons from the neutral beam. The primary proton beam was absorbed

    by a beam dump.

    Another three dipole magnets were placed in the region of Z = 14 to 93m from the target, to

    remove charged particles from the beam, including upstream decay, muons from the beam dump,

    and interaction products.

    A Pb filter(NM2PB) at Z = 18.5 m converted photons in the neutral beam into e+e to remove

    them effectively.

    Two nearly parallel neutral beams were defined with a primary collimeter with two square holes

    placed at Z = 19.8 meters. A steel slab collimeter at Z = 38.8m prevented particles crossing from

    one beam to the other.

    At Z = 85 m, a collimeter named the defining collimeter, which was made of steel, defined

    the final dimensions of the beams. The beams formed square dimensions of 0.5 mrad 0.5 mradfor the first part of the run(winter run) and 0.7 mrad 0.7 mrad for the second part of the

    15

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    TRD'S

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    Defining Collimator

    Slab Collimator(NM2CV1)

    BA

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    AVB B2 dipolesFinal Focus Quads

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    BlockHouse

    He He

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    Jaw Collimators

    18" decay pipe 30" decay pipe

    Spin Rotator Dipole

    00

    meters

    feet

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    10

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    NM2Q1-1 NM2Q1-2 NM2Q1-3 NM2Q2-1 NM2Q2-2 NM2Q2-3 NM2Q2-4 NM2D1-1 NM2D1-1 NM2D2

    NM2H

    AA

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    Beamstop(NM2BS)

    48" decay pipe

    30 cm BeO Target

    Eartly Sweeper (NM2S1)

    Beam elev. 733' 11"NM2WC3

    (Air SWIC)

    (NM2TGT)

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    Figure

    2.1:K

    TeV

    beamline

    anddetector

    layout.

    16

  • run(summer run), and their centers were separated by 1.6 mrad. The slab collimeter was removed

    in the summer run.

    At 90 m from the target, downstream of the defining collimator, there was a final sweeper

    magnet to remove charged particles produced in upstream decays or interaction. This provided a

    transverse momentum of 1.1 GeV/c. At this point, the beam mostly consisted of neutrons and KL.

    The ratio of neutron and K was approximately 3 and a small number of KS , , and remained

    in the beam.

    2.1.3 Vacuum System

    A vacuum pipe was located from Z = 22 to 159 meter and its inside was evacuated in order to

    reduce beam interaction with residual gas. The vacuum was kept at 1.0 106 torr.The downstream end of the vacuum pipe at Z = 159 m was sealed with a window, which was

    made of Kevlar web and aluminum mylar corresponding to 0.16% radiation lengths and diameter

    of 0.9 m.

    2.2 Detector

    This section describes functions of detector elements used in the KTeV experiment. This includes

    explanations of a spectrometer, a electromagnetic calorimeter, and veto system.

    The momentum of a charged particle was measured by a spectrometer which consisted of four

    drift chambers and a dipole magnet. The energy of a photon was determined with a calorimeter

    made of pure CsI crystals. The information of the track momentum and deposit energy of a charged

    particle was also used to discriminate a pion and a electron. Photons escaping from the detector

    was vetoed by photon veto counters placed at perimeters of the vacuum pipe, drift chambers, and

    the CsI calorimeter.

    2.2.1 Charged Spectrometer

    The KTeV charged spectrometer was located just downstream of the vacuum window. The main

    purpose of the spectrometer was to find trajectories of charged particles including the decay vertex

    and to measure the momentum of each charged track. In addition, the upstream chambers were

    used to provide fast trigger signals.

    The spectrometer consisted of four drift chambers(DC1 DC4) and an analysis magnet placed

    between DC2 and DC3. Positions and dimensions of each drift chamber and the analysis magnet

    are shown in Table 2.1. The position resolution of the drift chambers was about 100m and a

    nominal momentum resolution was 0.5 %. Helium bags filled between the drift chambers to reduce

    the effect of multiple scattering, photon conversion and beam interaction in the spectrometer.

    17

  • 20 cm

    100 120 140 160 180Distance from Target (m)

    TriggerHodoscopes

    2 KL beams

    TRD

    Vacuum Decay Region

    Vacuum Window

    Analysis Magnet

    DriftChambers

    MuonCounters

    MuonFilter

    Hadron Vetowith Lead Wall

    CsIPhoton Veto Detectors

    Figure 2.2: KTeV E799-II Detector. This is a schematic view of the detector region, as a down-

    stream part of Figure 2.1. Note the scale of Z direction, corresponding the position from the target,

    is shrunk.

    Table 2.1: Positions and dimensions of the spectrometer elements. Z positions are measured at

    upstream faces.

    Elements Z position(m) Aperture(width(m) hight(m))DC1 159.42 1.30 1.30DC2 165.57 1.64 1.44Magnet 170.01 2.90 2.00DC3 174.59 1.74 1.64DC4 180.49 1.90 1.90

    18

  • Drift Chamber

    Figure 2.3 shows the cross section of each drift chamber. Each chamber had four sense plane for

    the detection of signals from passing charged tracks. A upstream set of two sense wire planes in a

    chamber were strung vertically and used to detect X position(X view) and downstream sense wire

    planes were for the detection of Y position(Y view).

    12.7mm

    (0.1mm gold-plated aluminum)Window Guard Wire

    Sense Wire(0.025mm gold-plated tungsten)

    (0.1mm gold-plated aluminum)Field Wire

    Chamber window

    Chamber window

    Beam Direction

    t1, x1

    t2, x2

    Figure 2.3: A cross section of the drift chamber. This is a look-down view of the drift chamber.

    The wires oriented vertically in the front were used for the X position measurement, and the rear

    part strung horizontally was for the Y position measurement.

    The sense wires were 0.025 mm thick gold-plated tungsten and the field wires were 0.1 mm 6 ogold-plated aluminum. The field shaping wires were arranged in a hexagonal pattern around each

    sense wire and formed a hexagonal drift cell. The window guard wires were also 0.1 mm gold-plated

    aluminum, to maintain the field shape at the edge of drift cells. The sense wires in each sense plane

    were strung with a spacing of 12.7 mm(a half inch), and the adjacent sense planes were staggered

    by 6.35 mm with respect to the sense wire positions. This offset allowed us to resolve the left-right

    ambiguity of a particle.

    The chambers were filled with Argon/Ethane gas mixture. The gas was a 49.75% Argon,

    49.75% Ethane and 0.5% isopropyl alcohol mixture in the winter run, and proportion of isopropyl

    alcohol was raised to 1 % in the summer run for additional quenching. Alcohol in the gas absorbed

    19

  • damaging ultraviolet light at the signal amplification around the wire. With typical operating high

    voltage of negative 2450 V 2600 V on the cathodes and window wires, the drift velocity in each

    chamber was approximately 50m/ns.

    Pulses from the sense wires were amplified and discriminated by preamplifier cards mounted

    on the chamber. The discriminated signal was fed into LRS 3377 time to digital converters(TDCs)

    operated in a common stop mode, that is, the incoming signal from the sense wire started the TDC

    counting and all running TDCs were stopped by a common signal from a fast trigger(actually, Level

    1 trigger explained later). The TDC time distribution is shown in Figure 2.4. The in-time window

    was defined as 115 ns < t < 350 ns.

    0 100 200 300 400 500time(ns)

    In-time window

    EarlyLate

    1000

    2000

    3000

    4000

    5000

    6000

    7000

    8000

    Figure 2.4: TDC time distribution of drift chamber. The in-time window was defined as 115 ns

    < t < 350 ns. The sharp edge at 350 ns was short drift time near the sense wire. The tail at 200

    ns or less, which corresponded to a longer drift time, was due to hits very far from the sense wire

    and non-uniformity of the electric field. The slope between 200 ns and 270 ns shows non-linearity

    of the drift velocity far from the sense wire.

    The sharp edge at 350 ns corresponds to a short drift time near the sense wire. The tail at 200

    ns or less, which corresponded to a longer drift time, was due to hits very far from the sense wire

    and non-uniformity of the electric field. The slope between 200 ns and 270 ns shows non-linearity

    of the drift velocity far from the sense wire.

    The drift times were converted to drift distances and then to the position of the track at the

    chamber. For a hit pair of a proper single track, the sum of distances(SOD) of adjacent sense wires

    as seen x1 + x2 in Figure 2.3, can be determined and it must be equal to the offset of adjacent

    sense wires, 6.35 mm.

    The SOD distribution is shown in Figure 2.5. There is a clear peak at 6.35 mm. The width

    of the distribution, considered as a combined position resolution of two sense planes, was 150

    m assuming Gaussian distribution. It implies that the individual position resolution of the drift

    20

  • SOD(mm)6.35 7.355.35

    1000

    2000

    3000

    4000

    5000

    6000

    Figure 2.5: The sum of distance(SOD) distribution. The mean of SOD distribution corresponded

    to a half of a drift cell, 6.35 mm.

    chambers is 150m/

    2 ' 100m.

    Analysis Magnet

    The analysis magnet, a dipole magnet located between DC2 and DC3, provided a vertical magnetic

    field. The strength of the magnet field was about 2000 gausses over an aperture of about 2 meters.

    This gave a transverse momentum kick in horizontal direction of 205 MeV/c to charged particles.

    Momentum Resolution

    The momentum resolution of the KTeV spectrometer was measured to be a quadratic sum,

    pp

    = 0.016% p 0.38%, (2.1)

    where p is the momentum of a charged particle in GeV/c and p is its deviation. The constant

    term was due to the multiple scattering. The term linear in momentum is due to the finite position

    resolutions of the drift chambers, whose contribution becomes larger for tracks with smaller bending

    angle.

    2.2.2 Trigger hodoscopes

    Two planes of scintillator hodoscopes named V(upstream) and V(downstream) were used at the

    trigger level to select events with charged particles. The V hodoscope was located at Z = 183.90

    m while V was located at Z = 183.95 m. Both banks had dimensions of 1.9 m 1.9 m and 1.0 cmthick. As shown in Figure 2.6, the scintillators were installed vertically and covered the fiducial

    region. Beam holes were cut to reduce the beam interaction. The scintillation counters irregularly

    21

  • V bank V bank

    1.9 m 1.9 m

    1.9

    m1.9 m

    Figure 2.6: The V and V trigger hodoscope planes. The V hodoscope located at Z = 183.90 m

    while V was at Z = 183.95 m. Both banks had dimensions of 1.9 m 1.9 m and 1.0 cm thick.The scintillation counters had different sizes so that there was no overlapping gap between V and

    V bank.

    had different widths and lengths so that there was no overlapping gap between V and V banks.

    This helped to reduce the overall inefficiency of V and V banks.

    2.2.3 Electromagnetic Calorimeter

    The KTeV CsI electromagnetic calorimeter primarily provided a precision energy measurement of

    electromagnetic particles, e and . In addition, the information of the relation between a particle

    momentum and deposit energy in the calorimeter was used to identify electrons from pions.

    The electromagnetic calorimeter was constructed of 3100 pure cesium iodide(CsI) crystals and

    located at 186m from the target. The dimension of the calorimeter was 1.9 m 1.9 m transverseto the beams.

    CsI Crystals

    The calorimeter was stacked with 2232 small CsI crystals(2.5 2.5 50.0 cm) for the inner partand 868 large CsI crystals(5.0 5.0 50.0 cm) for the outer part, as shown in Figure 2.7. Thedepth of the crystals corresponded to 27 radiation lengths, to capture photon and electron showers

    completely. The depth of crystals was also 1.4 nuclear interaction lengths so that most of hadrons

    such as charged pions passed the calorimeter as minimum ionizing particles but some made a

    hadronic shower in the calorimeter.

    Each crystal was individually wrapped with 13m-thick aluminized mylar and black mylar to

    tune the response uniformity to the level of 5%.

    The scintillation light from the CsI crystal was conducted to photomultiplier tubes(PMT)

    22

  • 0.5 m

    1.9 m

    1.9 m

    Beam Direction

    Figure 2.7: The KTeV electromagnetic calorimeter. The calorimeter had dimensions of 1.9 m(W)

    1.9 m(H) 0.5 m(D) and located at 158m from the target. The calorimeter was constructed from3100 blocks of pure cesium iodide(CsI) crystals which were 2232 small CsI crystals(2.5 2.5 50.0cm) for the inner part and 868 large CsI crystals(5.0 5.0 50.0 cm) for the outer part.

    23

  • instrumented on the downstream end of each crystal. PMTs were operated at -1200V high voltage

    typically, resulting a gain of 5000. These PMTs showed a response linearity within the level of

    0.5% at the typical operation. The opening window of the PMT was a UV transmitting glass to

    accommodate the emission spectrum of the fast component of the scintillation light from the CsI

    crystal.

    The PMTs were mounted on the crystals with two layers of transparent RTV rubber filters,

    and 1 mm-thick glass UV filter between them to remove slower components of the CsI scintillation

    light.

    Readout System

    A digital PMT base(DPMT) system was used to read out the signals from the PMTs. One

    DPMT card was attached just behind each CsI crystal. Since the DPMT digitized the signals

    right after PMT, it enabled us noise-free data collection, without transmitting analog pulses for

    long distance. The DPMT consisted of a high voltage divider for the PMT, a charge integrating

    and encoding(QIE) circuit, an 8-bit flash ADC, and a driver-buffer-clock(DBC) circuit[14]. The

    QIE and DBC devices were custom integrated circuits designed for this calorimeter.

    The QIE was a hybrid digital/analog circuit integrating the charge from the PMT anode signal.

    To achieve both wide sensitivity range and sufficient precision, the QIE, with the help of the flash

    ADC, encoded the charge into an exponential form, i.e., 8 bits for the mantissa and 4 bits for the

    exponent.

    Each QIE had four identical circuits and used them in a round-robin manner. Since the circuit

    was synchronized to the Tevatron RF and the operation was completed in one clock cycle, each

    period of the charge integration was about 19 nsec, referred as a slice. This feature allowed

    non-deadtime readout. The output of the QIE was the analog signal and sent to the flash ADC

    for digitization.

    Performance

    Figure 2.8 shows a E/p distribution for electrons in Ke3 events, where E means a deposit energy

    in the CsI calorimeter and p means the electron momentum measured with the spectrometer. The

    intrinsic energy resolution of the calorimeter is shown in Figure 2.9 as a function of the momentum.

    This can be roughly parameterized as a quadratic sum;

    EE

    = 0.45% 2%E(GeV)

    . (2.2)

    2.2.4 Photon Vetoes

    In order to detect escaping photons and electrons away from the detector sensitive region, such as

    the drift chambers and CsI calorimeter, ten photon veto counters were placed transverse to the

    beam. They kept hermeticity for the decay products.

    24

  • Energy/Momentum

    Electrons from Ke

    0

    2000

    4000

    6000

    8000

    10000

    x 10 3

    0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2E/P

    Nevents = 1.92E+08E/P = 0.75 %

    Figure 2.8: E/p for electrons in Ke3 de-

    cays, where E means an energy deposit in the

    calorimeter, and p denotes a momentum mea-

    sured by the spectrometer.

    (Energy)/Energy vs. Momentum

    Electrons from Ke

    0

    0.002

    0.004

    0.006

    0.008

    0.01

    0.012

    0.014

    0.016

    0.018

    0.02

    0 10 20 30 40 50 60 70P (GeV)

    (E

    )/E

    Figure 2.9: The calorimeter intrinsic energy

    resolution measured in Ke3 events as a func-

    tion of electron momentum.

    25

  • Table 2.2: Positions and dimensions of the photon vetoes.

    Elements Z position(m) Aperture(m) Outer Dimension(m)

    RC6 132.596 0.84 0.84 1.00 (radius)RC7 138.598 0.84 0.84 1.00 (radius)RC8 146.598 1.18 1.18 1.44 (radius)RC9 152.600 1.18 1.18 1.44 (radius)RC10 158.599 1.18 1.18 1.44 (radius)SA2 165.116 1.540 1.366 2.500 2.500SA3 173.985 1.692 1.600 3.000 2.400SA4 180.018 1.754 1.754 2.372 2.372CIA 185.191 1.842 1.842 2.200 2.200CA 185.913 0.150 0.150 0.180 0.180

    Ring counters(RC6-RC10) were located inside the vacuum pipe. These had a rounded outer

    shape to fit the vacuum pipe and square apertures, and were azimuthally divided into 16 modules.

    Each of them consisted of 24 scintillator-lead layers and approximately corresponded to 16 radiation

    lengths.

    There were three Spectrometer Antis(SA2-SA4) surrounding DC2-4, respectively. The Ce-

    sium Iodide Anti(CIA) was also placed just upstream of the CsI calorimeter. These counters were

    rectangular in both the inner aperture and the outer shape. The amount of the material of them

    corresponded to 16 radiation lengths.

    The Collar Anti(CA) was a veto counter which defined a fiducial area at the beam holes of the

    CsI calorimeter. It consisted of the three layers of counters and 2.9 radiation lengths of tungsten,

    and located in front of the calorimeter.

    2.2.5 Hadron/Muon vetoes

    At the downstream of the calorimeter, there were detector components to veto hadrons, muons

    and particles through beam holes of the calorimeter. The dimensions and the Z positions of these

    detectors are shown in Table 2.3.

    Hadron Anti

    A 15 cm thick lead wall was located Z = 188.5m, just downstream of the CsI calorimeter, to cut

    off the small electromagnetic shower leakage from the calorimeter and to produce hadron showers.

    A scintillator bank called Hadron Anti(HA) followed the lead wall, to veto events including

    hadrons. There was a hole in the beam region of HA and the lead wall, to let neutral beams pass

    through without interaction.

    26

  • 100cm

    Figure 2.10: The schematic view of RC6, fac-

    ing downstream. The beam passed through

    the inner aperture. The perimeter of outer cir-

    cle fit right with the vacuum pipe. The other

    RCs were basically similar in a form but the

    dimensions seen in Table 2.2.

    237.2cm

    Figure 2.11: SA4 from upstream.

    CA

    Figure 2.12: The Collar Anti just in front of the calorimeter.

    27

  • 2.24m

    2.24m

    Figure 2.13: The HA hodoscope, which was

    composed of the same size of 28 scintillation

    counters. This followed the lead wall and de-

    tects hadronic particles.

    299c

    m

    378cm

    Figure 2.14: The Mu2 counter.

    Table 2.3: Positions and dimensions of the detectors(downstream of the calorimeter).

    Elements Z position(m) Dimensions(m)

    Lead wall 188.53(0.15m thick) 2.43 2.43HA 188.97 2.24 2.24Steal 1 189.09(1m thick) 2.4 2.4BA 191.09 0.60 0.30Steal 2 191.74(3m thick) 4.3 3.4MU2 194.83 3.93 2.99Steal 3 195.29(1m thick) 3.5 3.6MU3 196.36 3.00 3.00

    28

  • Muon Counter

    Downstream of the HA, there was a stack of steel totaling roughly 5 m-thick followed by Muon

    Veto Counter(MU2) which consisted of a scintillation hodoscope to reject events including muons.

    The MU2 had large dimensions, 2.99 m 3.78 m. The MU2 was used at the trigger level in thisanalysis.

    2.3 Trigger

    This section briefly describes the trigger system in the KTeV experiment. Main purpose of the

    trigger is to select signal events of interest and to reduce the event rate to an acceptable level for

    the data acquisition system.

    First, physics related triggers are explained. This trigger system had three levels; the first(Level

    1) and second(Level 2) were formed by a hardware logic, and the third was software filtering(Level

    3). The Level 1 trigger, which consisted of fast trigger sources, synchronized to the Tevatron RF(53

    MHz) and provided a deadtimeless trigger. The Level 2 performed time consuming decisions such

    as counting the number of hits in DCs, and the number of photons in the calorimeter. The

    Level 3 trigger carried out complex event reconstructions including charged track trajectories,

    energy clusters in the calorimeter, and simple vertex finding. The Level 3 filtering is explained in

    Section 2.4, as a part of the data acquisition system. The trigger for the signal basically required

    the existence of four charged tracks and allowed some additional particles such as photons.

    In addition, calibration triggers were used to collect events necessary for the CsI calibration

    and pedestal measurements.

    2.3.1 Level 1 Trigger

    In about 20 seconds of Tevatron spill, the primary proton beam and the secondary KL beam

    arrived with a microstructure, called a bucket, 1 2 nsec beam pulse once every 19 nsec. TheLevel 1 trigger, based on fast trigger sources such as photomultiplier signals, was synchronized to

    the microstructure and allowed deadtimeless triggering.

    There were 80 Level 1 trigger sources in total which were made with NIM logic. Table 2.4

    shows major Level 1 trigger sources used to take data for KL +e+e and KL +0D.After resynchronizing to the Tevatron RF before triggering, the trigger sources were transfered to

    twelve memory lookup units and decision was made simultaneously for 16 trigger outputs for each

    RF clock cycle.

    Next, we describe the Level 1 sources.

    29

  • Table 2.4: The E799 four track trigger elements.

    Trigger Element Trigger Level Description

    GATE 1 Vetoes fast neutrino pings

    3V TIGHT 1 3 hits in both V and V banks2DC12 MED 1 3 out of 4 DC1 and DC2 planes with 2 hits, 1 plane with 1 hitET THR1 1 ETOTAL 11GeVMU2 1 Veto events with 1 hit (15 mV, 0.2 mip) in MU2PHV 1 Veto events with 500MeV in PHV or events

    with 400MeV in the SACA 1 Veto events with 14GeV in the Collar-Anti34 HCY 2 require 3 hits in DC1Y, 3 hits in DC2Y

    and 4 hits in DC3Y, 4 hits in DC4YHCC GE2 2 require 2 HCC clustersYTF UDO 2 YTF trigger: Requires a good track in the upper half

    and a good track in lower half or one good central track

    3HC2X 2 3 hits in DC2X Bananas

    Neutrino Ping

    When the KTeV experiment was running, Tevatron also provided the primary proton beam to

    the other experiments. The Neutrino Ping signal was introduced to reject a fast, short-width

    high intensity spill for a neutrino-scattering experiment. This is because if fast high intensity

    beam happened to be delivered to the KTeV beam line, it could cause unacceptable high detector

    activity.

    Trigger hodoscope

    The V and V were used to detect charged track hits. We required at least 3 hits in both the V

    and V hodoscopes in this analysis.

    DC-OR trigger

    DC1 and DC2 were also used as a fast trigger source. Although the maximum drift time was about

    200 ns, the track is always passing between two wires in two adjacent planes, so that one of the hits

    should arrive within 100 ns after track passing. Therefore, we could utilize the logical OR of the

    wires for the fast trigger source. The trigger source consisted of sets of 16 OR-ed sense wires(10.2

    cm wide) and looked at the hit them in the X and Y views.

    This trigger source called DC-OR was used to select events with charged particles passing

    between DCs and V and V banks. The signal trigger required that three out of four planes had

    30

  • at least 2 hits, and the rest had at least one hit.

    Etotal

    An analog sum of the signals from all PMTs in the CsI calorimeter was used as a Level 1 trigger

    source. This approximately corresponded to total in-time energy deposit in the calorimeter. In

    this study, the energy deposit was required to be over 11GeV nominal.

    Muon Counters

    The muon counters were also used to veto events. Since both the signal and normalization modes

    do not include any muons, we vetoed events with any hits(0.2 mip) on the MU2 veto counter.

    Photon Vetoes

    Signals from the photon veto counters were also used to veto events with outgoing decay products

    from the fiducial volume. We vetoed if photons or electrons hit the photon vetoes and had an

    energy deposit of 500MeV or larger in the ring counters(RC6-10), or 400MeV or larger in the

    spectrometer anti(SA2-4). For the collar anti(CA), events were vetoed if particles hit CA and

    there was an energy deposit of over 14GeV.

    2.3.2 Level 2 Trigger

    The Level 2 trigger system is briefly explained here. Details can be found in Ref. [15] if one needs

    more explanation.

    The Level 2 trigger consisted of a slower trigger logic. This allowed us to do a simple event

    reconstruction for further background and accidental event reduction. When an event was accepted

    by Level 1, the Level 2 trigger decided if the event should be accepted to be sent to the DAQ/Level

    3 system, or not.

    Drift Chamber Activity(Kumquat)

    This trigger required hits which were identified as proper track hits in Y view of drift chambers.

    In this analysis, the drift chamber hit in a 205 ns gate was required in Y view for the trigger level;

    at least 3 hits each in DC1Y and DC2Y, and at least 4 hits each in DC3Y and DC4Y.

    Hardware Cluster Counter

    The hardware cluster counter [16] counted the number of in-time clusters in the CsI calorimeter.

    The hardware cluster was defined as a cluster consisting of crystals which had the energy deposit

    of 1GeV or more with a shared perimeter. Therefore, the particle associated with the hardware

    cluster was identified to be a electron or photon. This counting was achieved with a hard-wired

    31

  • energy cluster search algorithm and PMT outputs. We required at least two hardware clusters in

    the event.

    YTF trigger

    The function of Y Track Finder(YTF) [17] trigger made a simple Y track reconstruction by looking

    at hit-patterns in the drift chamber. For the momentum balance, we required the existence of

    reconstructed tracks in both upper and lower halves of chambers.

    Sum of Distance Correlation(Banana)

    This trigger equipment was used to require events with in-time hits in the drift chambers. The

    hits were assumed to be in-time if the sum of distances was in an allowed region. The time of each

    hit was measured with 625 MHz TDCs.

    At least three proper hits in DC2-X were required in this analysis.

    2.3.3 Trigger Rate

    During the winter run, the beam intensity was about 4 1012 protons per spill, where the beamduration was about 19 sec. For four track trigger containing KL +e+e and KL +0D,the trigger rate was about 25 kHz for the Level 1 trigger and about 2 kHz for the Level 2 trigger(70

    kHz for Level 1 and 7 kHz for Level 2 of total trigger rate). The DAQ live time was typically 60

    70%, depending on the beam rate and instantaneous beam intensity.

    2.3.4 Calibration Trigger

    The calibration trigger involved the following: laser calibration of the CsI calorimeter; pedestal

    measurements in all the detectors; uniformity measurements of the CsI by using cosmic muons.

    They were generated from local logic circuits.

    The trigger of laser calibration was formed by a flash of laser/dye system(5 Hz on- and off-spill).

    The pedestal was collected by opening ADC gates intentionally both on-spill and off-spill at

    the rate of 3 Hz.

    There were additional muon telescopes located at the top and bottom of the CsI blockhouse

    for triggering and positioning the cosmic muon event. The rate of this trigger was about 30 Hz,

    and it was taken during off-spill only. These events were used to measure the CsI uniformity in

    response along the Z direction.

    2.4 Data Acquisition System

    After performing event selection at the L1/L2 triggers, data were sent to KTeV data acquisition

    system(DAQ). In the KTeV experiment, the event rate after the Level 2 trigger was approximately

    32

  • 11 KHz and the average event size was 8 KBytes nominal, equal to about 2 GBytes per spill(11KHz8KBytes20sec/spill). The system was designed to handle twice this level of bandwidth.

    Here, we glance over the DAQ and Level 3 filtering. More details are found in Ref. [18, 19].

    2.4.1 Frontend and DAQ

    Memory Memory

    Memory

    Memory Memory MemoryMemory

    SGIChallenge

    Challenge

    SGIChallenge

    SGI

    SGI

    4 Planes

    6 Streams

    Challenge

    Memory

    1st Event sub-sub-event 2event 1sub-

    event 3 event 4 event 5sub-event 6

    sub-

    2nd Event

    Memory MemoryMemoryMemory Memory

    Memory Memory

    Memory

    Memory MemoryVME

    VME

    sub-

    VME

    VME

    Memory MemoryMemory MemoryMemory Memory

    RS485 lines

    Figure 2.15: Data acquisition system. Three planes were used for Level 3 trigger and the other

    was for online monitoring of the detector performance and online calibration.

    In Figure 2.15, the basic structure of the DAQ is drawn. An event, which consisted of six

    subevents at the frontend, was asynchronously read out through a fast data bus. The data was then

    sent to buffer memories(streams) through six RS485 lines, whose bandwidth was 40Mbytes/sec/line

    each. The buffer memory had a capacity of 4GB, large enough to store all the events collected

    over a spill, approximately 2GB.

    Each stream formed plane, which was logically connected to a Unix workstation(SGI Chal-

    lenge). The Unix work stations performed the event reconstruction for the filtering and monitoring:

    Three of four planes were used for the Level 3 filtering, and the other was used for monitoring of

    the detector response and online calibration.

    2.4.2 Level 3 filtering

    The level 3 filtering provided a simple event reconstruction with a software filtering on SGI Chal-

    lenges. This allowed us to reduce the trigger rate based on the information from sets of detector

    elements such as charged track and vertex reconstruction, particle identification with calorimeter

    E/p, and muon counter hits.

    33

  • The Level 3 filter for our study required three reconstructed tracks shared a vertex which

    located from 90.0 to 158.0 meters from the target.

    2.5 Physics Run

    This section describes the data collected in the KTeV-E799II runs, which was used for physics

    analysis of KL +e+e and KL +0D.The data used in this measurement consisted of two runs of KTeV-E799II experiment, winter

    run and summer run. The winter run was performed between February 1 and March 23, 1997,

    run 8245 through 8910. The summer run was between July 24 and September 3, 1997, run 10463

    through 10970.

    There were some differences between the winter and the summer runs, as shown in Table 2.5.

    The main difference between them was the proton beam intensity and neutral beam size. The

    proton beam intensity was lowered during the summer run due to the sharing of the proton beam

    in the Tevatron with other experiments. To keep appropriate kaon beam intensity, the larger

    neutral beams were used in the summer run to compensate for the decreased intensity of the

    primary proton beam.

    Table 2.5: The KTeV-E799II run conditions.Winter Run Summer Run

    Run Number 8245-8910 10463-10970

    Proton Intensity(spill) 5.0 1012 3.5 1012Beam Size at the CsI 10 cm10 cm 12 cm12 cm4 Track L1 Trigger Rates 20 KHz 23 KHz

    4 Track L2 Trigger Rates 1.5 KHz 2.3 KHz

    The collected data were written to about 500 Digital Linear Tapes(DLT) at the experiment.

    Each DLT stored about 10GB of data. Since they included all physics triggers, we split off only 4

    track tagged events into 38 DLTs for the winter and 44 DLTs for the summer runs. Furthermore,

    the data of 82 4 track triggered tapes were processed in a step. This separated and filtered the

    4 track triggered events into datasets which were used for a different analysis. The filtering was

    performed with offline event reconstruction code. This stage reduced the total data size to 17

    DLTs. In our ana